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Entropy 2017, 19(7), 308; doi:10.3390/e19070308

Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization

1
School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
2
School of Engineering, RMIT University, Melbourne 3000, Australia
*
Author to whom correspondence should be addressed.
Received: 30 April 2017 / Revised: 23 June 2017 / Accepted: 24 June 2017 / Published: 28 June 2017
(This article belongs to the Special Issue Information Geometry II)
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Abstract

Information geometry enables a deeper understanding of the methods of statistical inference. In this paper, the problem of nonlinear parameter estimation is considered from a geometric viewpoint using a natural gradient descent on statistical manifolds. It is demonstrated that the nonlinear estimation for curved exponential families can be simply viewed as a deterministic optimization problem with respect to the structure of a statistical manifold. In this way, information geometry offers an elegant geometric interpretation for the solution to the estimator, as well as the convergence of the gradient-based methods. The theory is illustrated via the analysis of a distributed mote network localization problem where the Radio Interferometric Positioning System (RIPS) measurements are used for free mote location estimation. The analysis results demonstrate the advanced computational philosophy of the presented methodology. View Full-Text
Keywords: information geometry; statistical manifolds; nonlinear estimation; natural gradient; maximum likelihood estimation information geometry; statistical manifolds; nonlinear estimation; natural gradient; maximum likelihood estimation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Cheng, Y.; Wang, X.; Moran, B. Optimal Nonlinear Estimation in Statistical Manifolds with Application to Sensor Network Localization. Entropy 2017, 19, 308.

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